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Optimal Reconfigurable Intelligent Surface Placement in Millimeter-Wave Communications


Abstract and Figures

In this work, we examine the use of reconfigurable intelligent surfaces (RISs) to create alternative paths from a transmitter to a receiver in millimeter-wave (mmWave) networks, when the direct link is blocked. In this direction, we evaluate the end-to-end signal-to-noise ratio (SNR) expression of the transmitter-RIS-receiver links that take into account the transmitter-RIS and RIS receiver distances and enable us to acquire important insights regarding the RIS position that maximizes it. Finally, the insights are corroborated by numerical results.
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Optimal Reconfigurable Intelligent Surface
Placement in Millimeter-Wave Communications
Konstantinos Ntontin, Dimitrios Selimis, Alexandros-Apostolos A. Boulogeorgos, Antonis Alexandridis,
Aris Tsolis, Vasileios Vlachodimitropoulos, and Fotis Lazarakis
Institute of Informatics and Telecommunications, National Centre for Scientific Research "Demokritos", Greece,
e-mail: {konstantinos.ntontin, dselimis, aalex, atsolis, vvlachod, flaz }
Department of Digital Systems, University of Piraeus, Greece, e-mail:
Abstract—In this work, we examine the use of recon-
figurable intelligent surfaces (RISs) to create alternative
paths from a transmitter to a receiver in millimeter-wave
(mmWave) networks, when the direct link is blocked. In
this direction, we evaluate the end-to-end signal-to-noise
ratio (SNR) expression of the transmitter-RIS-receiver
links that take into account the transmitter-RIS and RIS-
receiver distances and enables us to acquire important
insights regarding the RIS position that maximizes it.
Finally, the insights are corroborated by numerical results.
Increasing data-rate demands have led current mobile-access
networks relying on sub-6 GHz bands reach their limits in
terms of available bandwidth. This bottleneck created the need
to examine above-6 GHz bands for mobile-access networks.
Currently, bands in the lower-end mmWave spectrum are used
for point-to-point and point-to-multipoint line-of-sight (LOS)
wireless backhaul/fronthaul and fixed-wireless access net-
works [1]. Such deployments span the 30-100 GHz operational
frequency range. However, the expected migration of future
mobile-access networks to the 30-100 GHz band pushes the
corresponding wireless backhaul/fronthaul links towards the
beyond-100 GHz bands. Due to this, backhauling/fronthauling
transceiver equipment vendors have performed LOS trials in
the D band (130-174.8 GHz), which showcase the potential of
using it in such deployments [2]. Apart from LOS, street-level
deployments in dense urban scenarios necessitate devising
non-LOS (NLOS) solutions since LOS links may not always
be ensured. However, despite the fact that according to mea-
surements [3], [4] NLOS communication through scattering
and reflection from objects in the radio path is feasible in the
30-100 GHz range, the higher propagation loss of beyond-100
GHz bands is likely to put such communication into question.
The conventional approach of counteracting NLOS links
is by providing alternative LOS routes through relay nodes
[5]. Although this is a well-established method to increase the
coverage when the signal quality of the direct links is low, it is
argued that it cannot constitute a viable approach for massive
deployment, especially for mmWave networks. This is due to
the increased power consumption of the active radio-frequency
(RF) components in high frequencies that relays need to
be equipped with [6]. Apart from relaying, communication
through passive non-reconfigurable specular reflectors, such as
dielectric mirrors, has been proposed as another alternative.
Such a method for coverage enhancement has the potential
to be notably more cost efficient compared with relaying
and has been documented at both mmWave and beyond-100
GHz bands [6], [7]. Due to the highly dynamic nature of
blockage at high frequencies, it would be desirable that such
reflectors can change the angle of departure of the waves
based on changing blockage conditions so that they direct the
beams towards different routes. However, passive reflectors
are incapable of supporting the aforementioned functionality
since the conventional Snell’s law applies. Based on the above,
an intriguing question that arises is: Would it be possible to
deploy reconfigurable reflectors that can arbitrarily steer the
impinging beam based on dynamic blockage conditions? The
answer is affirmative by considering the RIS paradigm.
RISs are two-dimensional structures of dielectric material,
in which tunable reflecting elements are embedded [8–11].
They constitute a substantially different technology than re-
laying, owing to their independence from bulky and power-
hungry analog electronic components, such as power ampli-
fiers and low-noise amplifiers. Additionally, their operation,
in contrast with relaying, does not require dividers and com-
biners, which can incur high insertion losses. By individually
tuning the phase response of each individual RIS element, the
reflected signals can constructively aggregate at a particular
focal point, such as the receiver. Such a tuning can be
enabled by electronic phase-switching components, such as
PIN diodes, RF-microelectromechanical systems, and varactor
diodes, that are introduced between adjacent elements [12].
Hence, RISs offer an alternative-to-relaying method for large-
scale beamforming without the incorporation of high power
consuming electronics and insertion losses involved by the ad-
ditional circuitry. In practice, the RIS element phase shift can
be controlled by a central controller through programmable
software [12].
Motivation and contribution: Previous works on RISs
mostly consider NLOS channels with respect to the
transmitter-RIS and RIS-receiver links, which make them
rather suitable for sub-6 GHz omnidirectional communica-
tions. Likewise, the employed models assume that the whole
RIS surface is illuminated regardless of the transmitter-RIS
distance. However, due to the fact that RISs in future networks
are expected to cover large portions of sizeable structures, such
as buildings, only a portion of the total RIS area would be illu-
minated, which depends on the aforementioned distance. Such
a reasoning necessitates the derivation of a novel expression
of the end-to-end SNR that incorporates such a dependence.
Based on the above, in this work we derive the corresponding
SNR expression in a mmWave RIS-aided link and use it to
extract important insights regarding the RIS placement that
maximizes the resulting expression. Furthermore, the findings
are validated by means of numerical simulations.
The rest of this work is structured as follows: In Section
II, we present the scenario under consideration together with
its main assumptions. In Section III, we derive the resulting
end-to-end SNR expression, which we use to extract important
insights regarding the optimal positioning of the RIS. Numeri-
cal results that validate the theoretical findings are provided in
Section IV, whereas Section V concludes this work and gives
ideas for future work.
In this section, we first present the scenario under consid-
eration and, subsequently, the main assumptions.
A. Scenario
We consider a communication between a street-level trans-
mitter and receiver, as depicted in Fig. 1, in a mmWave highly
directional link1. The transmitter and receiver are equipped
with large, with respect to the wavelength, antennas that enable
communication through highly directive beams. Furthermore,
we assume that due to a fixed or moving obstacle the direct
communication is not possible, which can be the case for
highly directive beams and large carrier frequencies. In such
a case, the transmitter redirects the beam to an RIS mounted
on some fixed structure, such a tall building. The RIS acts a
beamformer by adjusting the phase response of the elements
so that the beam is directed towards the receiver. Moreover, we
consider that both the transmitter-RIS and RIS-receiver links
are subject to LOS conditions and that the RIS is located in
the far field of both the transmit and receive antennas.
B. Main Assumptions
We consider that the size of the RISs in the network is
sufficiently large so that the area illuminated by the main
lobe of a transmitted beam is smaller than RIS area. Such
an assumption is justified by the fact that it is expected that
RISs in future networks are going to cover large portions
of the building facades. In addition, their size needs to be
sufficiently large so that they can simultaneously accommodate
the transmissions of different transmitters. By considering
that under pencil-beam transmissions almost all the transmit
energy is located in the half-power beamwidth area (HPBW)
of the main lobe [6] and that the main-lobe shape is conical,
1As pointed out in Section I, such a link could be a fixed point-to-point
link of an upcoming beyond-100 GHz backhaul/fronthaul network.
Transmitter Receiver
Fig. 1: Communication through an RIS.
Fig. 2: Illuminated RIS area.
approximately a circular area of the RIS is illuminated by the
transmission2with radius rRIS , given by
rRIS =tan φT x
2rT x,RIS ,(1)
where φT x is the HPBW of the transmitted beam and rT x,RIS
is the distance between the centers of the transmitter and
the RIS, as depicted in Fig. 2. By assuming, without loss of
generality, a parabolic reflector as a transmit antenna with a
diameter DT x, it approximately holds that [13]
φT x 1.22 λ
DT x
Consequently, the illuminated RIS area, which is denoted
by SRIS , can be approximated by
SRIS πr2
RIS .(3)
Finally, we assume that the received signal is subject to
additive white Gaussian noise. Its power level in dBm for a
bandwidth W, denoted by N0, is equal to
N0=174 + 10 log10 (W) + FdB,(4)
2The actual shape of the illuminated RIS area depends on the angle of
incidence of the impinging wave on the RIS. It is a circle for angle of incidence
equal to 0and an ellipse for angles greater than 0, according to the theory
of conical cross sections. However, in this work our primary focus is on the
resulting SNR expression and the optimal RIS positioning based on it, where
the latter does not depend on the shape of the RIS illuminated area. Due to
this, we consider the circular footprint model in order to simplify the final
SNR expression.
where FdB is the noise figure in dB and Wis the transmission
bandwidth [14].
In this section, we firstly compute the received SNR of the
considered RIS-aided communication. Subsequently, based on
the expression, we comment on the optimal RIS placement.
Proposition 1: By assuming that all the RIS elements have
the same amplitude reflection coefficient, denoted by Γ, the
maximum received power, which we denote by Prmax , can be
approximated as
PT xtan4φT x
2Γ2GT xGRx cos θ(arr )
0cos θ(dep)
×rT x,RIS
rRIS,Rx 2
where PT x is the transmit power. GT x is the gain of the
transmit antenna, GRx is the gain of the receive antenna, θ(arr)
is the incidence angle on the RIS, θ(dep)
0is the departure angle
from the RIS, and rRIS,Rx is the distance between the centers
of the RIS and the receiver.
Proof : See Appendix A.
Assuming parabolic reflector antennas at the transmitter and
the receiver with diameters DTx and DRx, respectively, it
holds that
em, m ={T x, Rx},(6)
where eT x and eRx are the aperture efficiencies of the transmit
and receive parabolic reflectors, respectively.
As a result, the equivalent end-to-end SNR at the receiver
can be approximated as
Ptxtan4φT x
2Γ2GT xGRx cos θ(arr )
0cos θ(dep)
×rT x,RIS
rRIS,Rx 2
Remark 1: Based on (7), an important question that arrises
is whether a transmitter should focus its beam towards an
RIS that is closer to the transmitter or closer to the receiver.
From (7), we observe that the SNR expression depends on the
transmitter-RIS and RIS-receiver distances through the ratio
rT x,RIS
rRIS,Rx and the terms cos θ(arr)
0and cos θ(dep)
0. The latter
holds since the angles of incidence θ(arr)
0and departure θ(dep)
depend on rT x,RIS and rRIS,Rx. In particular, for an RIS
with axis parallel to the ground (without loss of generality)
the closer the RIS to the transmitter is, the smaller the angle
of arrival and the larger the angle of departure are, with
respect to the RIS normal. The opposite holds the closer
the RIS to the receiver is. Hence, targeting an RIS that is
closer to the transmitter or to the receiver would roughly have
the same effect on the value of the term cos θ(arr)
0cos θ(dep)
that is included in (7). As a result, the equivalent end-to-end
SNR expression is expected to be mainly determined by the
value of the ratio rT x,RIS
rRIS,Rx . The particular ratio reveals that the
hTx hRx
Transmitter Receiver
Fig. 3: 2D simulation setup.
transmitter should target an RIS that is closer to the receiver
than the transmitter so that the equivalent end-to-end SNR is
The aim of this section is to validate Remark 1 regarding
the optimal RIS positioning that maximizes the end-to-end
equivalent SNR by means of simulations. Towards this, we
consider the 2D point-to-point simulation setup that is depicted
in Fig. 3, in which the axis of the RIS is parallel to the ground.
According to the considered geometry, it holds that
rT x,RIS =qr2
T x,RIS hor + (hRIS hT x )2,
rRIS,Rx =q(rT x,Rx,hor rT x,RIS hor )2+ (hRIS hRx )2,
0=tan1rT x,RIS,hor
hRIS hT x ,
0=tan1|rT x,Rx,hor rT x,RI Shor |
hRIS hRx .
TABLE I: Parameter values used in the simulation.
f140 GHz
PT x 1 W
W2 GHz
FdB 10 dB
rT x,Rx,hor 40 m
hRIS 15 m
hT x,hRx 3 m
DT x,DRx 10 cm
eT x,eRx 1
In Table I, we present the considered values for the involved
parameters in the simulation3.
3The value hRIS = 15 m can be a typical value for an RIS that is located
in the top of a 5-floor building facade by considering that the height of each
floor is around 3 m. In addition, the values hT x =hRx = 3 m can typically
correspond to transmitter and receiver nodes that are mounted on lampposts.
0 10 20 30 40 50 60
rTx,RIS,hor [m]
SNR [dB]
Fig. 4: SNR vs. the horizontal transmitter-RIS distance.
0 10 20 30 40 50 60
rTx,RIS,hor [m]
SRIS [m2]
Fig. 5: RIS area vs. the horizontal transmitter-RIS distance.
Regarding the optimal direction of towards a large RIS
surface that the transmitter should focus its beam on or,
from another perspective, the optimal placement of an RIS,
in Fig. 4 we illustrate the SNR as a function of the horizontal
transmitter-RIS distance, where the SNR is computed accord-
ing to (7). As we observe from Fig. 4, for SNR maximization
the transmitter should focus its beam on a point on the RIS
area that is very close to the receiver. Hence, Remark 1 is
validated. Moreover, we observe that substantial SNR gains,
in particular more than 20 dB, are achieved by the optimal
beam focusing compared with, for instance, the focusing on
the point on the RIS area that is vertically above the transmitter
(rT x,RIS,hor = 0). In addition, in Fig. 5 we illustrate SRIS as a
function of the horizontal transmitter-RIS distance. We observe
that at the distance for which the maximum SNR is obtained
the corresponding illuminated RIS area is approximately equal
to 1 m2. Consequently, this showcases the feasibility of such
a deployment since RIS surfaces with areas much larger than
1m2can be installed onto large building facades. Finally, we
note that in the simulated scenario the illuminated RIS area
is located in the far field of both the transmit and receive
antennas, as it is required in our model. This is due to the
fact that the Fraunhofer distance is equal to 2D2
m= 10 m,
m={T x, Rx}, for both the transmit and receive antennas
and the minimum distance between the possible RIS location
and the aforementioned antennas is equal to 12 m.
We have conducted this work in order to determine the
optimal RIS placement with respect to the transmitter and
receiver antenna positioning. Towards this, we have considered
a realistic mmWave scenario in which the RIS area that is
illuminated by the transmitted very directional beam is smaller
than the total RIS area, which is expected in forthcoming RIS
deployments. Based on this model, we have quantified the
equivalent end-to-end SNR, which reveals that the RIS should
be optimally placed closer to the receiver than the transmitter
so that the SNR is maximized. Such an analytical outcome
was validated by means of simulations, which showed that
substantial gains are expected by the optimal deployment.
Future work will focus on the comparison of an RIS- and a
relay-aided point-to-point scenario in terms of coverage prob-
ability and rate, where the optimal deployments are considered
for both cases.
This work has reveived funding from the H2020 ARIADNE
project (Grant Agreement no. 871464).
A. Proof of Proposition 1
The incident wave on the RIS nth element is given by
Einc,n =Eincej2π
λrT x,RISnˆ
where rT x,RISnis the distance between the transmitter and
the nth element of the illuminated RIS area. Considering that
the spatial power density of the incident electric wave on the
nth element of the RIS is approximately4equal to PT xGT x
it holds that E2
2η=PT xGT x
where ηis the free-space impedance. The captured power by
the nth element, denoted by Pcap,n, of the RIS is given by
Pcap,n =E2
2ηAeff ,n =λ
4π2PT xGT x GRIS,n θ(arr)
where Aeff,n =λ2
4πGRIS,n θ(arr)
0is the effective aperture
of the nth RIS element with GRIS,n θ(arr)
0being its gain.
Based on the passive reflector theory, it holds that [13]
GRIS,n θ(arr )
λ2dxdycos θ(arr)
where dxand dyare the x and y-axis dimensions of each RIS
element, respectively. The term dxdycos θ(arr)
the projected surface on the RIS seen by the transmitter.
4Considering that rT x,RISnrT x,RI S due to the far-field operation.
The spatial power density at the receiver antenna after re-
flection from the nth element, which is denoted by Prspatial,n ,
is given by
Prspatial,n =Pcap,n
Γ2GRIS,n θ(dep)
PT xΓ2GT x GRIS,n θ(arr)
0GRIS,n θ(dep)
T x,RIS r2
where, as in the transmission towards the RIS case, it is
assumed that due to the far-field positioning of the receiver
antenna with respect to the RIS it holds that rRISn,Rx
rRIS,Rx , where rRISn,Rx is the distance from the center of
the nth RIS element to the center of the receiver antenna.
In addition, GRIS,n θ(dep)
0is the gain of the nth RIS
element involved in the radiation towards the receiver antenna.
Similarly to (12), it holds that
GRIS,n θ(dep)
λ2dxdycos θ(dep)
where the term dxdycos θ(dep)
0represents the projected
surface on the RIS seen by the receiver.
Next, by assuming that the nth RIS element through its
corresponding switching element is adjusted so that the phase
of the departing beam related with the element is equal to
φRIS nand that mutual coupling among different elements
is negligible, the electric field of the impinging beam at the
receiver antenna, which we denote by Er,n, is given by
Er,n =Er,ne
j φRISn+2π(rT x,RI Sn+rRISn,Rx )
Er,n =q2ηPrspatial,n
PT xΓ2GT x GRIS,n θ(arr)
0GRIS,n θ(dep)
T x,RI S r2
The received power PrφRIS1, ..., φRISMxMyconsidering
the contribution from all the RIS elements is given by
rφRIS1, ..., φRI SMxMy
n=1 Er,n
4π4PT xΓ2GT x GRx
T x,RIS r2
n=1 rGRIS,n θ(arr)
0GRIS,n θ(dep)
j φRISn+2π(rT x,RI Sn+rRISn,Rx )
where Mxand Myare the number of RIS elements in the x-
and y-axis, respectively.
From (17), it is evident that the received power is maximized
by setting
φRISn=2π(rT x,RI Sn+rRISn,Rx )
By taking into account that
n=1 rGRIS,n θ(arr)
0GRIS,n θ(dep)
=GRIS θ(arr )
0GRIS θ(dep)
GRIS θ(s)
λ2SRIS cos θ(s)
0, s ={arr, dep},(20)
and by using (1) and (3), the maximum value of
PrφRIS1, ..., φRI SMxMy,Prmax , is approximated by (5),
which concludes the proof.
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The future of mobile communications looks exciting with the potential new use cases and challenging requirements of future 6th generation (6G) and beyond wireless networks. Since the beginning of the modern era of wireless communications, the propagation medium has been perceived as a randomly behaving entity between the transmitter and the receiver, which degrades the quality of the received signal due to the uncontrollable interactions of the transmitted radio waves with the surrounding objects. The recent advent of reconfigurable intelligent surfaces in wireless communications enables, on the other hand, network operators to control the scattering, reflection, and refraction characteristics of the radio waves, by overcoming the negative effects of natural wireless propagation. Recent results have revealed that reconfigurable intelligent surfaces can effectively control the wavefront, e.g., the phase, amplitude, frequency, and even polarization, of the impinging signals without the need of complex decoding, encoding, and radio frequency processing operations. Motivated by the potential of this emerging technology, the present article is aimed to provide the readers with a detailed overview and historical perspective on state-of-the-art solutions, and to elaborate on the fundamental differences with other technologies, the most important open research issues to tackle, and the reasons why the use of reconfigurable intelligent surfaces necessitates to rethink the communication-theoretic models currently employed in wireless networks. This article also explores theoretical performance limits of reconfigurable intelligent surface-assisted communication systems using mathematical techniques and elaborates on the potential use cases of intelligent surfaces in 6G and beyond wireless networks.
Full-text available The relatively unused millimeter-wave (mmWave) spectrum offers excellent opportunities to increase mobile capacity due to the enormous amount of available raw bandwidth. This paper presents experimental measurements and empirically-based propagation channel models for the 28, 38, 60, and 73 GHz mmWave bands, using a wideband sliding correlator channel sounder with steerable directional horn antennas at both the transmitter and receiver from 2011 to 2013. More than 15,000 power delay profiles were measured across the mmWave bands to yield directional and omnidirectional path loss models, temporal and spatial channel models, and outage probabilities. Models presented here offer side-by-side comparisons of propagation characteristics over a wide range of mmWave bands, and the results and models are useful for the research and standardization process of future mmWave systems. Directional and omnidirectional path loss models with respect to a 1 m close-in free space reference distance over a wide range of mmWave frequencies and scenarios using directional antennas in real-world environments are provided herein, and are shown to simplify mmWave path loss models, while allowing researchers to globally compare and standardize path loss parameters for emerging mmWave wireless networks. A new channel impulse response modeling framework, shown to agree with extensive mmWave measurements over several bands, is presented for use in link-layer simulations, using the observed fact that spatial lobes contain multipath energy that arrives at many different propagation time intervals. The results presented here may assist researchers in analyzing and simulating the performance of next-generation mmWave wireless networks that will rely on adaptive antennas and multiple-input and multiple-output (MIMO) antenna systems.
IRS is a new and revolutionizing technology that is able to significantly improve the performance of wireless communication networks, by smartly reconfiguring the wireless propagation environment with the use of massive low-cost passive reflecting elements integrated on a planar surface. Specifically, different elements of an IRS can independently reflect the incident signal by controlling its amplitude and/or phase and thereby collaboratively achieve fine-grained 3D passive beamforming for directional signal enhancement or nulling. In this article, we first provide an overview of the IRS technology, including its main applications in wireless communication, competitive advantages over existing technologies, hardware architecture as well as the corresponding new signal model. We then address the key challenges in designing and implementing the new IRS-aided hybrid (with both active and passive components) wireless network, as compared to the traditional network comprising active components only. Finally, numerical results are provided to show the great performance enhancement with the use of IRS in typical wireless networks.
Technical Report
In this paper, we perform a system-level feasibility analysis of full-duplex (FD) relay-aided cellular networks that are equipped with multiple antennas at the base stations (BSs) and relay nodes (RNs). The aim is to understand whether FD relaying is capable of enhancing the rate of cellular networks. With the aid of tools from stochastic geometry, we develop a tractable approach for computing the percentile rate, which allows us to gain insights on the impact of FD relaying for both cell-edge and cell-median mobile terminals (MTs) subject to network interference. Contrary to previous works that do not take into account the network interference, the framework reveals that even in the absence of self interference at the FD RNs a network with half-duplex (HD) RNs can outperform its FD counterpart for a moderate number of antennas at the BSs and RNs. On the other hand, the FD-based network can substantially outperform both the HD-based one and the one without RNs for a sufficiently large number of antennas at the BSs and RNs and substantially small self-interference power effect at the RNs. Finally, the aforementioned analytical insights are validated by means of Monte Carlo simulations.
As the cellular networks continue to progress between generations, the expectations of 5G systems are planned towards high capacity communication links that can provide users access to numerous types of applications (e.g., augmented reality, holographic multimedia streaming). The demand for higher bandwidth has led the research community to investigated unexplored frequency spectrum, such as the terahertz-band for 5G. However, this particular spectrum is strived with numerous challenges, which includes the need for Line-of-Sight (LoS) links as reflections will deflect the waves as well as molecular absorption that can affect the signal strength. This is further amplified when high Quality-of-Service (QoS) has to be maintained over infrastructure that supports mobility as users (or groups of users) migrate between locations, requiring frequent handover for roaming. In this paper, the concept of mirrorassisted wireless coverage is introduced, where smart antennas are utilised with dielectric mirrors that act as reflectors for the terahertz waves. The objective is to utilise information such as the user’s location, and to direct the reflective beam towards the highest concentration of users. A multi-ray model is presented in order to develop the propagation models for both indoor and outdoor scenarios, in order to validate the proposed use of the reflectors. An office and a pedestrian walking scenarios are used for indoors and outdoors scenarios, respectively. The results from the simulation work shows an improvement with the usage of mirror-assisted wireless coverage, improving the overall capacity, received power, path loss and probability of line of sight.